The announcement that Susan Philipsz had won the Turner prize – for a sound piece consisting of her own frailly beautiful voice singing a Scottish lament over the black waters of the Clyde – was rendered almost inaudible tonight by the chants and whoops of student protesters, who were separated from the champagne-sipping partygoers at Tate Britain only by a hastily erected barrier.

Students from London's art schools, including Chelsea College of Art & Design and Central Saint Martin's, had occupied the entrance hall of Tate Britain, where they demonstrated against the coalition government's cuts to the arts and humanities in higher education.

Those attending the award ceremony could not see the protesters, but they could certainly hear them.

Philipsz – herself a political activist before attending art school – said of the students: "My heart goes out to them. I really support them." Those who approached too close to the screens separating prize from protest were warned away by security guards "for your own safety".

Estimates of the number of students, who were protesting peacefully, varied between 60 and 200.

Ed Vaizey, the culture minister, who attended the ceremony, told the Guardian: "They have every democratic right to protest. I just wish they'd do some work."

Sir Nicholas Serota, the director of Tate, said "Everyone who cares about the arts is bound to be concerned by cuts to arts in higher education. Art schools have been laboratories for the kind of work that has gone on to win the Turner prize."

Philipsz, 45, is the first person in the history of the award to have created nothing you can see or touch. Instead, she sculpted her prizewinning work in sound – indeed from the sound of her own voice, singing a Scottish lament over the river Clyde in her hometown, Glasgow.

She was always the art-world favourite to win the £25,000 prize, the most prestigious – and frequently controversial – British art prize.

She beat competition from the other shortlisted artists: Dexter Dalwood, whose contemporary take on traditional history painting saw him an early bookies' favourite; Angela de la Cruz, whose mangled, dishevelled canvases place her somewhere between painter and sculptor; and the Otolith Group, whose work, often in film, encompasses curating as well as creating. Each of the runners up receives a £5,000 award.

The work for which she won the prize, though, was an installation made for the art festival Glasgow International in May. Beneath each of the three bridges in the city centre – the George V Bridge, the mighty Caledonian Railway Bridge and Glasgow Bridge – were installed recordings of Philipsz singing three slightly different versions of that same song heard in the Turner prize exhibition, in which a drowned lover returns to haunt their sweetheart.

The words are the same at first, then, as the verses go on, they veer off to take their own paths, returning to unison for the refrain.

Reactions to the protesters from those attending the ceremony were almost overwhelmingly sympathetic.

Artist Bob and Roberta Smith called the cuts "the biggest culture bashing since the book burnings of the 1930s and the dissolution of the monasteries".

Sculptor Richard Wilson said: "I think it shows super-intelligence to have done this on the night of the Turner prize. This is the only way to do it. They can't do it with a whisper, they must do it with a shout."

Novelist and critic Philip Hensher, one of the judges for this year's Turner prize, said: "They have a perfect right to protest and a right to seize a high-profile opportunity. If they did it in Richmond Park on a quiet afternoon no one would take any notice."

Leafleting outside Tate Britain was Gill Addison, a lecturer at the Chelsea College of Art. Addison said: "This demonstration is not in opposition to the Turner prize but about the fact that our arts and culture are in jeopardy.

"It's about the future of the Turner prize. How can it continue without artists being trained?"